<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="hilbert1.html#K1">HP-WFF</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="hilbert3.html#NM1">SetValuation</a>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hilbert3.html#M1" target="_self">Permutation</a> of <font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>, <a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>









<b>assume </b><a NAME="E1:50"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3">=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p2">(<span class="default"><a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T23">FUNCT_2:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T88">FUNCT_2:88</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K2">"</a> </span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="hilbert3.html#E1:50"><i><font color="Green">E40</font></i></a>, <a class="ref" href="hilbert3.html#T37" target="_self">Th37</a></i>
;<br/>


</div>
